Magus comma

Interval information

Ratio	50331648/48828125
Factorization	224 × 3 × 5-11
Monzo	[24 1 -11⟩
Size in cents	52.504148¢
Name	magus comma
Color name	salegu 4th, sg114
FJS name	[math]\text{6d4}_{5,5,5,5,5,5,5,5,5,5,5}[/math]
Special properties	reduced
Tenney height (log2 nd)	51.1262
Weil height (log2 max(n, d))	51.1699
Wilson height (sopfr(nd))	106
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~4.45241 bits
Comma size	medium
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The magus comma (ratio: 50331648/48828125, monzo: [24 1 -11⟩) is a medium 5-limit comma, which is the difference between:

• four classic chromatic semitones (25/24) and three classic diatonic semitones (16/15): (16/15)³/(25/24)⁴,
• three lesser dieses (128/125) and a classic chromatic semitone: (128/125)³/(25/24),
• a perfect fifth (3/2) and eleven classic major thirds (5/4), octave-reduced: 12/(5/4)¹¹, and
• the classic major seventh (15/8) and twelve classic major thirds, octave-reduced: 15/(5/4)¹².

Temperaments

Tempering out this comma leads to the magus and amigo temperaments.

See also

• Würschmidt comma
• Magic comma